Spectrum of definite type of self-adjoint operators in Krein spaces

Langer, Heinz and Langer, Matthias and Markus, Alexander and Tretter, Christiane (2005) Spectrum of definite type of self-adjoint operators in Krein spaces. Linear and Multilinear Algebra, 53 (2). pp. 115-136. ISSN 0308-1087 (https://doi.org/10.1080/03081080500055049)

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Abstract

For a self-adjoint operator in a Krein space we construct an interval [ν, μ] outside of which the operator has only a spectrum of definite type and possesses a local spectral function. As a consequence, a spectral subspace corresponding to an interval outside [ν, μ] admits an angular operator representation. We describe a defect subspace of the domain of the angular operator in terms of the Schur complement, and we derive variational principles for the discrete eigenvalues in such intervals of definite type.

ORCID iDs

Langer, Heinz, Langer, Matthias ORCID logoORCID: https://orcid.org/0000-0001-8813-7914, Markus, Alexander and Tretter, Christiane;
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